💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined.$\frac{5-\frac{45}{a^{2}}}{\frac{3}{a}-1}$

$\frac{-5(a+3)}{a}, a \neq 0,3$

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 6

Complex Rational Expressions

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Oregon State University

McMaster University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

00:48

Simplify each complex rati…

00:38

01:49

02:01

01:46

02:59

01:35

03:02

02:55

01:50

Okay, We're going to simplify a complex expression. This is problem number 20. Our expression is five minus 45 over a squared all over three over a minus one. The first thing we're gonna dio on the top is we're going to simplify that little bit farther. In order to do that, we need to put the five over a squared. And so we're gonna have to multiply the five by a squared subtract 45 over a squared, which ends up giving us five a squared minus 45 all over a squared. Now we need to simplify the Dominator too. So we have three a minus and you can turn the one into a over a so we're gonna have three minus a over a and we're gonna do five a squared finest 45 over a squared. And when you divide, you can multiply by the reciprocal. Okay, so we're gonna factor out on the numerator. Ah, we're gonna make it five a squared minus nine. All over a squared times. The a over three minus a. We can get rid of one of the ace. At least us with five. A squared minus nine. All over a times three minus a. That's factor out. The A squared minus nine gives us five a minus three A plus three. And on the bottom, Let's take out a negative of the three minus a and make this a negative, eh? And that's gonna give us a minus three. Okay, That means we can go ahead and eliminate a minus three, leaving us with five times a plus three all over. Negative, Eh? So that is as far as we can go. A sw far simplifying. And we also know that a cannot be zero. It cannot be three. Otherwise, it turns out to be undefined.

View More Answers From This Book

Find Another Textbook

In mathematics, the absolute value or modulus |x| of a real number x is its …

Simplify each complex rational expression. In each case, list any values of …

00:35

In $3-38$ write each expression in simplest form. Variables in the radicand …

02:22

In $27-39,$ factor each polynomial completely.$$x^{4}-81$$

02:26

In $3-20,$ solve each equation and check.$$\frac{2 x}{3}+1=\frac{3 x…

05:28

In $3-12,$ multiply and express each product in simplest form. In each case,…

01:26

In $9-26,$ write each expression as the product of two binomials.$$a…

03:59

Simplify each expression. In each case, list any values of the variables for…

00:59

In $13-22,$ solve each equation or inequality. Each solution is an integer. …

02:57

In $15-26,$ find and graph the solution set of each inequality.$$|2-…

11:11

Amanda drove 40 miles. Then she increased her rate of speed by 10 miles per …

02:32

In $3-14,$ solve and check each inequality.$$\frac{2}{x}+\frac{3}{x}…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.